BLOOD FLOW TRANSPORT THROUGH AN ELASTIC VESSEL BY THE VIBRO-VOLUMETRIC METHOD. PART 1: MATHEMATICAL MODEL
V.S. Sizikov1,2, A.P. Chupakhin3
1Saint Petersburg State Institute of Technology (Technical University), Saint Petersburg, Russia
2Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russia
3Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Keywords: vibro-volumetric method, perfusion, blood pumping, rheological model, viscoelastic fluid
Abstract
The process of blood pumping through an artificial vessel using a vibro-volumetric perfusion pump is investigated. The device is essentially an expanding channel with vibrating walls, approximating a diffuser in its simplest form. The relationship between the vibration parameters and the geometric characteristics of the device and the flow rate of transported blood is examined. A mathematical perfusion model is presented. This model incorporates a three-component rheological model of blood and a two-mass model of the oscillatory system of the device. The interaction between the vibrating walls, the deformable vessel, and the blood are also accounted for in the model presented.
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